Extremal determinants of Laplace–Beltrami operators for rectangular tori

Author:

Faulhuber Markus

Abstract

AbstractIn this work we study the determinant of the Laplace–Beltrami operator on rectangular tori of unit area. We will see that the square torus gives the extremal determinant within this class of tori. The result is established by studying properties of the Dedekind eta function for special arguments. Refined logarithmic convexity and concavity results of the classical Jacobi theta functions of one real variable are deeply involved.

Funder

University of Vienna

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

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